Here's the problem: indefinite integral of (-3x^2)/sqrt((t^3)-16)
If you are unsure of your result, use differentiation to check your result:
We can see it is close (essentially the wrong constant factor of the radical), but not quite right. I would let:
and so we have:
Now, checking by differentiation, we find:
The derivative of the anti-derivative is the original integrand, so our result is correct.